Solve for $x$ and $y$ using elimination. ${-5x+6y = -8}$ ${3x+3y = 51}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${-5x+6y = -8}$ $-6x-6y = -102$ Add the top and bottom equations together. $-11x = -110$ $\dfrac{-11x}{{-11}} = \dfrac{-110}{{-11}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {-5x+6y = -8}\thinspace$ to find $y$ ${-5}{(10)}{ + 6y = -8}$ $-50+6y = -8$ $-50{+50} + 6y = -8{+50}$ $6y = 42$ $\dfrac{6y}{{6}} = \dfrac{42}{{6}}$ ${y = 7}$ You can also plug ${x = 10}$ into $\thinspace {3x+3y = 51}\thinspace$ and get the same answer for $y$ : ${3}{(10)}{ + 3y = 51}$ ${y = 7}$